There are several requirements for a physical reservoir to efficiently solve computational tasks. (i) High dimensionality is necessary to map inputs into a high-dimensional space. This property facilitates the separation of originally inseparable inputs in classification tasks and allows reading out spatiotemporal dependencies of inputs in prediction tasks. The dimensionality is related to the number of independent signals obtained from the reservoir. (ii) Nonlinearity is necessary for a reservoir to operate as a nonlinear mapping. This property allows inputs that are not linearly separable to be transformed into those that are linearly separable in classification tasks. It is also useful for effectively extracting nonlinear dependencies of inputs in prediction tasks. (iii) Fading memory (or short-term memory) [1]}, [2]}, [3]} is necessary to ensure that the reservoir state is dependent on recent-past inputs but independent of distant-past inputs. It is also referred to as the echo state property, indicating that the influence of past inputs on the current reservoir states and outputs asymptotically fades out [4]}, [5]}. Such a property is particularly important for representing sequential data with short-term dependencies. (iv) Separation property is required to separate the responses of a reservoir to distinct signals into different classes. On the other hand, a reservoir should be insensitive to unessential small fluctuations, such as noise, so that similar inputs are classified into the same class. Therefore, when a system parameter variation causes a transition between non-chaotic and chaotic regimes, it is often recommended that the parameter be set close to the transition point (the so-called edge of chaos [6]}, [7]}) where the transformation by a reservoir is neither very expanding nor very contracting.
